Probabilistic local waveform inversion for moment tensor and hypocentral location

We have developed a probabilistic method to determine simultaneously earthquake-source mechanism, hypocentral location and source time function (STF) from the inversion of short-period waveform data of weak local events (epicentral distance less than 100 km). The procedure takes into account the effects of the random noise contained in the seismograms, the uncertainty of the hypocentre determined from arrival times and the inaccurate knowledge of the velocity structure, while estimating the error affecting the derived focal parameters. The forward modelling of the seismic ground motion is computed for frequencies up to 5 Hz in horizontally layered elastic media. Assuming that all uncertainties can be described by Gaussian probability density functions (PDFs), a priori information, measurement errors and theoretical errors are estimated. Then, the proposed probabilistic approach maps the posterior PDFs for the hypocentral coordinates, the moment tensor, and the STF. The final estimates for the focal parameters are given by the maximum likelihood points of the PDFs, while solution uncertainties are presented by scatter density plots. The estimated uncertainties in the moment tensor components are plotted on the focal sphere in such a way, that the significance of the double couple, the compensated linear vector dipole and the volumetric parts of the source can be assessed. Tests of the method were first performed on synthetic data generated for a configuration of a local seismic network in Hungary. Simple point sources as well as complex mechanisms were successfully reconstructed. In the next step, real data from the region were inverted to obtain the mechanisms of three local earthquakes. The resulting moment tensor solutions have negligible volumetric part, implying the tectonic nature of the events. The retrieved source mechanisms are in agreement with the available clear readings of first-arrival P-wave polarities and with the main stress pattern published for the epicentral region.